### Algebra, Geometry and Combinatorics Day (AlGeCom) is a one day,
informal meeting of mathematicians from the
University of Illinois, Purdue University and nearby universities, with interests in algebra,
geometry and combinatorics (widely interpreted).

Further details will be posted here as they become available. Or you may
contact the University of Illinois organizers

Hal Schenck and

Alexander Yong, or the Purdue organizers

Uli Walther
and

Saugata Basu .

__Next event__ : Spring, 2010

**Date: **May 1 (Sat), 2010

###
** Location: ** Department of Mathematics, Purdue University.

The talks will held at MATH 175.

__Speakers and schedule__:

### Coffee and pastries **8h30**** **

### Nero Budur (Notre Dame) **9h30 - 10h30 **

Title: Local systems and singularities.

Abstract: The local systems on the complement of an arbitrary divisor

in a smooth complex projective variety contain a wealth of information

about the singularities of the divisor. We describe various

filtrations on local systems (Hodge, polar), their induced

stratifications on the space of unitary rank one local systems, and

their relation with the singularities of the divisor. Applications

include: some results about Hodge numbers of abelian covers, and some

results about singularity invariants (Hodge spectra, b-functions, and

topological zeta functions) for hyperplane arrangements. This surveys

joint work with various people.

Title: Discrete integrable evolutions and noncommutative cluster algebras

Abstract: I will explain to to generalize the notion of a cluster mutation to

the non-commutative case, by using what we know about cluster algebras related

to integrable discrete evolutions. Special cases of noncommutativity include,

but are more general than, quantum cluster algebras related to canonical basis

[c.f. Berenstein, Zelevinsky].

### Ben Howard (Michigan) **14h - 15h **

Title: The relations among invariants of ordered points on the projective line

Abstract: We consider the coordinate rings of GIT quotients of n points on the

projective line modulo automorphisms of the line. We describe generators and

relations. Kempe found generators in 1894. We find the ideal of relations in

these generators (based on joint work with John Millson, Andrew Snowden, and

Ravi Vakil.)

Coffee and snacks **15h30**

Title: On the Computation of the Cohomology of Complex Algebraic Varieties

Abstract: We consider the algorithmic problem of computing the (singular) cohomology

of a complex algebraic variety from a set of defining equations.

The best known algorithms solving this problem run in double exponential

time. We report on partial results towards single exponential time algorithms, in particular

concerning the zeroth cohomology and the smooth projective case. We shall give some

ideas about these algorithms, describe how good degree bounds yield efficient algorithms,

and what is used to prove such bounds.**Food**

There are many restaurants within walking distance to the campus (including Indian, Chinese, Irish, Middle-eastern, Thai, Japanese, Korean, Vietnamese, Mexican etc.). There are also several coffee-houses in and around campus as well as across the river in the town of Lafayette. See here for dining options in the Lafayette-West Lafayette area.

We will go for dinner on Sat evening at 6.30 to the Nine Irish Brothers.

**Accommodation**

We have reserved a block of rooms at the Union Club Hotel which is conveniently located on campus and a two-minutes walk to the Mathematics department. **Parking**Parking is free on Saturdays on campus. The most convenient parking garage is on N. University street adjacent to the Math building.